LudovicoVan
Posts:
4,165
From:
London
Registered:
2/8/08


Re: Matheology § 300
Posted:
Jul 7, 2013 4:32 PM


"Michael Klemm" <m_f_klemm@tonline.de> wrote in message news:krchad$adn$1@solani.org... > Julio Di Egidio wrote: > >> Again, that for all n in N the value is 1/oo just does not entail that >> the limit is 1/oo. > > If you accept that 1/oo is a natural not > depending on the natural n, then the limit n>oo of > the constant sequence (1/oo, 1/oo, ...) is 1/oo. > The way how the number 1/oo is obtained > doesn't matter.
Well, I do not see how that can be acceptable. The original expression has a subexpression dependent on n under the limit, not just a constant value. Again, that the sequence is constant for all n in N does not entail that the limit for n>oo must be equal to that constant value.
Indeed, by your token:
lim_{n>oo} Card(N\F(n)) = oo (1)
yet:
lim_{n>oo} N\F(n) = {} (2)
or is that supposed to be N, too??
At least, I suppose we'd agree that:
lim_{n>oo} F(n) = N (3)
Of course, I am assuming that the limit of the cardinality of our wellfounded sequence is equal to the cardinality of the limit of the sequence. I still do not see how we could define the limit otherwise (I may be missing formal details), but even less I can see (1) compatible with (2).
Julio

